Internal problem ID [3516]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 260.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } x^{2}-\left (y a +x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x) = (x+a*y(x))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x}{a \ln \left (x \right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 22
DSolve[x^2 y'[x]==(x+a y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{-a \log (x)+c_1} y(x)\to 0 \end{align*}